AQL Number Sense and Algebraic Thinking 2 — Questions and Answers
Question 1: If f(x) = 2x² - 3x + 1, what is f(2)?
- 3 (Correct answer)
- 5
- 7
- 9
Correct answer: 3
Substituting x = 2: f(2) = 2(4) - 3(2) + 1 = 8 - 6 + 1 = 3.
Question 2: Which property is demonstrated by: 5(3 + 4) = 5(3) + 5(4)?
- Commutative property
- Associative property
- Distributive property (Correct answer)
- Identity property
Correct answer: Distributive property
The distributive property states that a(b + c) = ab + ac, which is exactly what is shown here.
Question 3: What is the greatest common factor (GCF) of 36 and 48?
- 6
- 12 (Correct answer)
- 18
- 24
Correct answer: 12
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and factors of 48 include 12 and 24; the greatest shared factor is 12.
Question 4: A car travels 180 miles in 3 hours. What is the average speed in miles per hour?
- 45 mph
- 54 mph
- 60 mph (Correct answer)
- 90 mph
Correct answer: 60 mph
Average speed = distance ÷ time = 180 ÷ 3 = 60 mph.
Question 5: Simplify: (x³y²)(x²y⁴)
- x⁵y⁶ (Correct answer)
- x⁶y⁸
- x⁵y⁸
- x⁶y⁶
Correct answer: x⁵y⁶
Multiply by adding exponents of like bases: x^(3+2) = x⁵ and y^(2+4) = y⁶, giving x⁵y⁶.
Question 6: Which of the following represents a linear equation?
- y = x²
- y = 2x + 5 (Correct answer)
- y = x³ - 1
- y = 1/x
Correct answer: y = 2x + 5
y = 2x + 5 is linear because the variable x is raised only to the first power and the graph is a straight line.
Question 7: If a rectangle has a length of 9 cm and a width of 5 cm, what is the area?
- 28 cm²
- 40 cm²
- 45 cm² (Correct answer)
- 50 cm²
Correct answer: 45 cm²
Area of a rectangle = length × width = 9 × 5 = 45 cm².
AQL Number Sense and Algebraic Thinking 2
If f(x) = 2x² - 3x + 1, what is f(2)?